Aikhenvald (2000): Classifiers — A Typology of Noun Categorization Devices

@cite{aikhenvald-2000} @cite{greenberg-1972} @cite{dixon-1982}

Aikhenvald, Alexandra Y. (2000). Classifiers: A Typology of Noun Categorization Devices. Oxford Studies in Typology and Linguistic Theory. Oxford University Press.

Cross-linguistic typology of noun categorization systems following Aikhenvald's 7-property schema (A–G, §1.5). The schema (NounCategorizationSystem) lives in Typology/ClassifierSystem.lean; per-language data in Fragments/{Lang}/ClassifierSystem.lean.

This file aggregates the 7 currently-formalized systems (French/Italian/Mandarin/Japanese/Xhosa/Shona/Swahili) and verifies typological properties from @cite{aikhenvald-2000} (Tables 10.17, 15.1, 15.2) and @cite{greenberg-1972}'s classifier-number complementarity over that sample. None of the theorems below are universals over the abstract NounCategorizationSystem type — they are sample-restricted empirical claims; adding a counterexample language to the sample is the right way to falsify them.

Western Armenian is intentionally excluded from the main allSystems sample: it is non-obligatory with no unmarked default, and the Aikhenvald-style sample-restricted findings (sample_all_obligatory, sample_all_have_default) are about the obligatory-classifier subspace. Armenian appears separately in optionalClassifierSystems.

Chierchia-anchored claims about Mandarin/Japanese type-shift blocking are in Studies/NMP.lean (chronologically older paper, separate study file). The Greenberg classifier-number complementarity claim appears here (Aikhenvald §15 cites Greenberg) and is refined in Studies/LittleMoroneyRoyer2022.lean (CLF-for-N vs CLF-for-NUM split).

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abbrev Aikhenvald2000.french : Typology.NounCategorizationSystem

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• Aikhenvald2000.french = Fragments.French.classifierSystem

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abbrev Aikhenvald2000.italian : Typology.NounCategorizationSystem

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• Aikhenvald2000.italian = Fragments.Italian.classifierSystem

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abbrev Aikhenvald2000.mandarin : Typology.NounCategorizationSystem

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• Aikhenvald2000.mandarin = Fragments.Mandarin.classifierSystem

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abbrev Aikhenvald2000.japanese : Typology.NounCategorizationSystem

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• Aikhenvald2000.japanese = Fragments.Japanese.classifierSystem

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abbrev Aikhenvald2000.xhosa : Typology.NounCategorizationSystem

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• Aikhenvald2000.xhosa = Fragments.Xhosa.classifierSystem

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abbrev Aikhenvald2000.shona : Typology.NounCategorizationSystem

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• Aikhenvald2000.shona = Fragments.Shona.classifierSystem

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abbrev Aikhenvald2000.swahili : Typology.NounCategorizationSystem

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• Aikhenvald2000.swahili = Fragments.Swahili.classifierSystem

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abbrev Aikhenvald2000.westernArmenian : Typology.NounCategorizationSystem

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• Aikhenvald2000.westernArmenian = Fragments.Armenian.classifierSystem

def Aikhenvald2000.allSystems : List Typology.NounCategorizationSystem

The seven obligatory-classifier systems formalized so far.

Equations

• Aikhenvald2000.allSystems = [Aikhenvald2000.french, Aikhenvald2000.italian, Aikhenvald2000.mandarin, Aikhenvald2000.japanese, Aikhenvald2000.xhosa, Aikhenvald2000.shona, Aikhenvald2000.swahili]

theorem Aikhenvald2000.sample_all_obligatory (s : Typology.NounCategorizationSystem) : s ∈ allSystems → s.IsObligatory

Languages whose Fragment is in allSystems are all obligatory.

theorem Aikhenvald2000.sample_all_have_default (s : Typology.NounCategorizationSystem) : s ∈ allSystems → s.HasUnmarkedDefault

Languages in the sample all have an unmarked default classifier/class.

theorem Aikhenvald2000.french_is_noun_class : Typology.NounCategorizationSystem.isNounClassType Fragments.French.classifierSystem.classifierType = true

theorem Aikhenvald2000.mandarin_is_classifier : Typology.NounCategorizationSystem.isClassifierType Fragments.Mandarin.classifierSystem.classifierType = true

theorem Aikhenvald2000.japanese_is_classifier : Typology.NounCategorizationSystem.isClassifierType Fragments.Japanese.classifierSystem.classifierType = true

theorem Aikhenvald2000.mandarin_inventory_from_fragment : Fragments.Mandarin.classifierSystem.inventorySize = 15

theorem Aikhenvald2000.japanese_inventory_from_fragment : Fragments.Japanese.classifierSystem.inventorySize = 36

theorem Aikhenvald2000.classifier_systems_have_default : Fragments.Mandarin.classifierSystem.HasUnmarkedDefault ∧ Fragments.Japanese.classifierSystem.HasUnmarkedDefault

theorem Aikhenvald2000.sample_classifier_no_agreement_nounclass_agreement : (∀ s ∈ allSystems, Typology.NounCategorizationSystem.isClassifierType s.classifierType = true → ¬s.HasAgreement) ∧ ∀ s ∈ allSystems, Typology.NounCategorizationSystem.isNounClassType s.classifierType = true → s.HasAgreement

@cite{aikhenvald-2000} Table 15.1, sample-restricted: classifier-type systems lack agreement; noun-class systems have agreement.

theorem Aikhenvald2000.fr_mandarin_jp_agreement_split : Fragments.French.classifierSystem.HasAgreement ∧ ¬Fragments.Mandarin.classifierSystem.HasAgreement ∧ ¬Fragments.Japanese.classifierSystem.HasAgreement

French has agreement; Mandarin and Japanese do not (Table 15.1).

theorem Aikhenvald2000.fr_mandarin_jp_assignment_split : Fragments.Mandarin.classifierSystem.assignment = Typology.AssignmentPrinciple.semantic ∧ Fragments.Japanese.classifierSystem.assignment = Typology.AssignmentPrinciple.semantic ∧ Fragments.French.classifierSystem.assignment = Typology.AssignmentPrinciple.mixed

Numeral classifier systems have purely semantic assignment; the noun-class system has mixed assignment (@cite{aikhenvald-2000} Table 15.2).

theorem Aikhenvald2000.mandarin_japanese_prefer_shape : (Fragments.Mandarin.classifierSystem.preferredSemantics.any fun (x : Typology.SemanticParameter) => x == Typology.SemanticParameter.shape) = true ∧ (Fragments.Japanese.classifierSystem.preferredSemantics.any fun (x : Typology.SemanticParameter) => x == Typology.SemanticParameter.shape) = true

East Asian classifier systems prefer physical properties (shape) — partial witness for Aikhenvald's cross-linguistic generalization.

theorem Aikhenvald2000.mandarin_japanese_have_animacy : (Fragments.Mandarin.classifierSystem.preferredSemantics.any fun (x : Typology.SemanticParameter) => x == Typology.SemanticParameter.animacy) = true ∧ (Fragments.Japanese.classifierSystem.preferredSemantics.any fun (x : Typology.SemanticParameter) => x == Typology.SemanticParameter.animacy) = true

Animacy is attested in both Mandarin and Japanese classifiers.

theorem Aikhenvald2000.fr_inventory_smaller_than_clf_inventories : Fragments.French.classifierSystem.inventorySize < Fragments.Mandarin.classifierSystem.inventorySize ∧ Fragments.French.classifierSystem.inventorySize < Fragments.Japanese.classifierSystem.inventorySize

Mandarin/Japanese classifier inventories exceed French's noun-class inventory. @cite{aikhenvald-2000} Table 15.1 generalization.

theorem Aikhenvald2000.mandarin_japanese_scope_numeralNP : (Fragments.Mandarin.classifierSystem.scopes.any fun (x : Typology.CategorizationScope) => x == Typology.CategorizationScope.numeralNP) = true ∧ (Fragments.Japanese.classifierSystem.scopes.any fun (x : Typology.CategorizationScope) => x == Typology.CategorizationScope.numeralNP) = true

Numeral classifiers operate inside numeral/quantifier NPs.

theorem Aikhenvald2000.french_scope_agreement : (Fragments.French.classifierSystem.scopes.any fun (x : Typology.CategorizationScope) => x == Typology.CategorizationScope.headModifierNP) = true ∧ (Fragments.French.classifierSystem.scopes.any fun (x : Typology.CategorizationScope) => x == Typology.CategorizationScope.predicateArgument) = true

French (the noun-class member of the sample) operates in head-modifier and predicate-argument scopes.

theorem Aikhenvald2000.noun_class_more_interactions : have cats := [Typology.GrammaticalCategory.definiteness, Typology.GrammaticalCategory.number, Typology.GrammaticalCategory.case_, Typology.GrammaticalCategory.tenseAspect, Typology.GrammaticalCategory.possession]; have ncInteractions := List.filter (Typology.interacts Typology.ClassifierType.nounClass) cats; have clInteractions := List.filter (Typology.interacts Typology.ClassifierType.numeralClassifier) cats; ncInteractions.length > clInteractions.length

@cite{aikhenvald-2000} Table 10.17: noun classes interact with more grammatical categories than numeral classifiers. Verified against the framework-agnostic interacts table in Typology.NounCategorization.

theorem Aikhenvald2000.sample_greenberg_complementarity : (∀ s ∈ allSystems, Typology.NounCategorizationSystem.isClassifierType s.classifierType = true → ¬s.HasObligatoryNumber) ∧ ∀ s ∈ allSystems, Typology.NounCategorizationSystem.isNounClassType s.classifierType = true → s.HasObligatoryNumber

@cite{greenberg-1972}: numeral classifiers and obligatory number marking are in complementary distribution. Holds in the sample. Aikhenvald §15 endorses Greenberg's generalization; @cite{little-moroney-royer-2022} §3.4 refines it (CLF-for-N languages obey it, CLF-for-NUM languages — Ch'ol, Mi'gmaq — falsify it).

theorem Aikhenvald2000.mandarin_japanese_have_default_clf : Fragments.Mandarin.Classifiers.defaultClassifier.isDefault = true ∧ Fragments.Japanese.Classifier.defaultClassifier? = some Fragments.Japanese.Classifier.tsu

Mandarin and Japanese both have a semantically bleached default classifier (Mandarin 个 ge, Japanese つ tsu).

theorem Aikhenvald2000.specific_classifiers_motivated : ((List.filter (fun (x : Typology.ClassifierEntry) => !x.isDefault) Fragments.Mandarin.Classifiers.allClassifiers).all fun (x : Typology.ClassifierEntry) => decide (x.semantics.length > 0)) = true ∧ ∀ (c : Fragments.Japanese.Classifier), ¬c.IsDefault → ¬c.IsMensural → c.encodes ≠ []

Non-default classifiers always carry at least one semantic parameter.

theorem Aikhenvald2000.xhosa_is_noun_class : Typology.NounCategorizationSystem.isNounClassType Fragments.Xhosa.classifierSystem.classifierType = true

theorem Aikhenvald2000.shona_is_noun_class : Typology.NounCategorizationSystem.isNounClassType Fragments.Shona.classifierSystem.classifierType = true

theorem Aikhenvald2000.swahili_is_noun_class : Typology.NounCategorizationSystem.isNounClassType Fragments.Swahili.classifierSystem.classifierType = true

theorem Aikhenvald2000.xhosa_has_agreement : Fragments.Xhosa.classifierSystem.HasAgreement

theorem Aikhenvald2000.sample_bantu_inventory_within_aikhenvald_range : Fragments.Xhosa.classifierSystem.inventorySize ≤ 20 ∧ Fragments.Shona.classifierSystem.inventorySize ≤ 20 ∧ Fragments.Swahili.classifierSystem.inventorySize ≤ 20

The three sampled Bantu languages have inventories in the @cite{aikhenvald-2000} Table 15.1 noun-class range (≤ 20).

theorem Aikhenvald2000.bantu_have_prefix_realization : (Fragments.Xhosa.classifierSystem.realizations.any fun (x : Typology.SurfaceRealization) => x == Typology.SurfaceRealization.prefix) = true ∧ (Fragments.Shona.classifierSystem.realizations.any fun (x : Typology.SurfaceRealization) => x == Typology.SurfaceRealization.prefix) = true ∧ (Fragments.Swahili.classifierSystem.realizations.any fun (x : Typology.SurfaceRealization) => x == Typology.SurfaceRealization.prefix) = true

def Aikhenvald2000.optionalClassifierSystems : List Typology.NounCategorizationSystem

Languages with non-obligatory classifier systems (per WALS Ch 55 optional). Western Armenian is the worked example (@cite{bale-khanjian-2014}). Kept separate from allSystems because the sample-restricted findings above are over obligatory systems — Armenian is precisely the kind of language those generalizations don't cover.

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• Aikhenvald2000.optionalClassifierSystems = [Fragments.Armenian.classifierSystem]

theorem Aikhenvald2000.westernArmenian_not_obligatory : ¬Fragments.Armenian.classifierSystem.IsObligatory ∧ ¬Fragments.Armenian.classifierSystem.HasUnmarkedDefault